K-theory for C*-algebras, and beyond

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 247 in Sci. Bldg. A

• Description : the pdf file

• Schedule : Wednesday 8.45 - 10.15
  

• Class dates :
  April 22, 29
  May 6, 13, 20, 27
  June 3, 10, 17, 24
  July 1, 8, 15, 22
  

• Lecture notes : Full document

• Weekly summaries : 1, 2, 3, 4, 5(1), 5(2), 6, 7, 8, 9, 10, 11, 12(1), 12(2), 13

• Overview : Motivation, Chap. I - IV,

• Student reports :
  Solution to Exercise 1.1.6, by Ikuya Ozeki
  Solution to Exercise 1.1.6, by Yoshiteru Murai
  Solution to Exercise 2.1.6, by Ikuya Ozeki
  Solution to Exercises 2.1.10, 2.2.2, 2.2.3 , by Ikuya Ozeki
  Solution to Exercise 2.2.2, by Kazumasa Narita
  Solution to Exercise 3.1.4, by Kazumasa Narita
  Solution to Exercise 3.1.5, by Shinya Kato
  Proof of Proposition 3.2.5, by Shinya Kato
  Solution to Exercise 3.3.3, by Naohiro Tsuzu
  Solution to Exercise 3.4.4, by Shinya Kato
  About GNS construction, by Ikuya Ozeki
  About unitization of C*-algebras, by Yoshihiko Terasawa
  Extension 6.3.4 on Fredholm operators and the index map, by Naohiro Tsuzu
  Introduction to topological K-theory, by Xuanrui Qi
  

• References : (electronic version available upon request)
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  [CMR07] J. Cuntz, R. Meyer, J. Rosenberg, Topological and bivariant K-theory, Oberwolfach Seminars, 36. Birkhauser Verlag, Basel, 2007.
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  [Ric15] S. Richard, Levinson's theorem: an index theorem in scattering theory, Proceedings of the Conference Spectral Theory and Mathematical Physics, Santiago 2014, Operator Theory Advances and Application, Birkhauser.
  [RLL00] M. Roerdam, F. Larsen, N. Laustsen, An introduction to K-theory for C*-algebras, London Mathematical Society Student Texts 49, Cambridge University Press, Cambridge, 2000.
  [Yos65] K. Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften 123, Academic Press, Inc., New York; Springer-Verlag, Berlin 1965.
  [W-O93] N.E. Wegge-Olsen, K-theory and C*-algebras, a friendly approach, Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993.